Abstract. This paper presents a general concept and mathematical framework of particle hygroscopicity distribution for the analysis and modeling of aerosol hygroscopic growth and cloud condensation nucleus (CCN) activity. The cumulative distribution function of particle hygroscopicity, H(κ, Dd) is defined as the number fraction of particles with a given dry diameter, Dd, and with an effective hygroscopicity parameter smaller than the parameter κ. From hygroscopicity tandem differential mobility analyzer (HTDMA) and size-resolved CCN measurement data, H(κ, Dd) can be derived by solving the κ-Köhler model equation. Alternatively, H(κ, Dd) can be predicted from measurement or model data resolving the chemical composition of single particles.

A range of model scenarios are used to explain and illustrate the concept, and exemplary practical applications are shown with HTDMA and CCN measurement data from polluted megacity and pristine rainforest air. Lognormal distribution functions are found to be suitable for approximately describing the hygroscopicity distributions of the investigated atmospheric aerosol samples.

For detailed characterization of aerosol hygroscopicity distributions, including externally mixed particles of low hygroscopicity such as freshly emitted soot, we suggest that size-resolved CCN measurements with a wide range and high resolution of water vapor supersaturation and dry particle diameter should be combined with comprehensive HTDMA measurements and size-resolved or single-particle measurements of aerosol chemical composition, including refractory components. In field and laboratory experiments, hygroscopicity distribution data from HTDMA and CCN measurements can complement mixing state information from optical, chemical and volatility-based techniques. Moreover, we propose and intend to use hygroscopicity distribution functions in model studies investigating the influence of aerosol mixing state on the formation of cloud droplets.